BRUSSELS, Belgium — Olli Rehn and Christine Lagarde used to be good at teamwork.

Lagarde, who heads the International Monetary Fund, was a member of the French synchronized swimming team in her youth. Rehn, the European Union's economic and monetary affairs commissioner, played soccer in Finland's top division.

Lately, however, both have raised doubts about whether they’re following the same game plan as they attempt to lead efforts to pull Europe out of its economic crisis.

Rehn, Lagarde and European Central Bank President Mario Draghi head the "troika" — the IMF, ECB and European Commission — that runs the multibillion-dollar bailout programs keeping the economies of Greece, Portugal, Ireland and Cyprus from going under.

They and the enforcers who work under them are also tasked with ensuring countries in the program comply with tough austerity measures aimed at bringing public finances under control in return for the bailout billions.

For angry citizens in the countries concerned, the troika and its "men in black" who fly in to supervise national policies have become a principal target of discontent.

In Portugal, a protest movement has sprung up under the banner: "Que se lixe a troika" — which politely translates as "Screw the Troika."

"We want to bring ideas together with the aim of defeating this government and all governments that collaborate with the troika program," the group said in a statement ahead of one demonstration in January.

Recently, however, the troika’s image as implacable, unquestionable and unified in its drive to steamroll governments into the application of its economic orthodoxy has started to fray.

For months, Lagarde's IMF has been signaling that its troika co-pilots have been too heavy handed in their pursuit of an austerity-driven solution to the recession.

Then last week, the IMF released a report acknowledging failings in the way the troika handled the first $145 billion bailout for Greece in 2010, notably by underestimating the economic pain awaiting the country and not forcing Greece's creditors to share that pain soon enough.

The report was partly a mea culpa, but it also suggested that much of the blame lay with European officials rather than the Washington-based fund. That provoked an angry response from the typically soft-spoken Rehn.

“I don’t think it’s fair and just for the IMF to wash its hands and throw the dirty water on the Europeans,” Rehn told a conference in Helsinki on Friday.

He archly reminded that as French finance minister at the time, Lagarde was among the European officials who opposed the financial "haircut" for Greek creditors that the IMF report now suggests was the better solution for Greece — and which finally happened in February 2012.

Rehn's spokesman Simon O'Connor said the European Commission "fundamentally disagrees" with IMF criticism suggesting it had underestimated the need for reforms in Greece to spur growth.

The very public spat between the IMF and the European Commission underscores deeper tensions within the troika.

Four years into the euro zone debt crisis, the IMF is now sending 56 percent of its loans to debt-stricken European countries. That's starting to annoy many of its contributing states, especially those in Asia and Latin America that resent relatively rich Europeans getting special treatment.

The European Commission, on the other hand, is being pulled in different directions by EU member governments. Northern countries led by Germany are demanding continued economic rigor while France leads those seeking a softer line on austerity and resisting unpopular reforms to free up the economy.

Given the tensions, some wonder whether the troika can, or should, carry on in its current form.

Jean Pisani-Ferry, a senior economic adviser to the French government, says the IMF and ECB should take smaller roles while the EU sets up its own European Monetary Fund to support euro zone members in trouble.

"Should the troika survive?" Pisani wrote in a column for the economic think-tank Bruegel. "It was perhaps inevitable that initially they worked jointly; but there is reason to question such an approach now."

Despite the squabbling, it's unlikely the troika will unravel. Nevertheless, the spat is adding to the feeling of disarray and division hanging over policymakers’ efforts to pull Europe out of recession.

Plans for a banking union in which EU members would work together to support or wind up failing banks — rather than force weak individual nations to bear the burden — appeared close to approval a year ago, but are now being held up by German objections.

French President Francois Hollande accused the European Commission of seeking to dictate to France after the EU executive body exercised its power to outline reforms for boosting growth.

"Where structural reforms are concerned, it's up to us and us alone to decide what path to take," Hollande said. Then he flew off to Tokyo, where his declaration on Sunday that the euro zone crisis was over baffled many in Europe struggling with record unemployment and a recession forecast to drag on well into 2014.

Even the crucial ECB decision to buy up bonds of euro zone countries in dire straits, which was credited with ending market panic last year, has been cast into doubt by a legal challenge in Germany's Constitutional Court that opened Tuesday.

Underscoring the divisions in Europe, the two German members of the ECB's governing board expressed starkly differing views on the issue at the court's opening hearing.

Perhaps Europe's policymakers would do well to reflect on the Russian origins of the word "troika" — a sled pulled by three horses. A popular subject in Russian art is of hungry wolves racing across snowbound steppes to devour passengers whose sleighs lose speed.

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